Finite Group Databasebeta

← #11889237

Subgroups — #11889237

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595244C211yesmaximal, characteristic
2#10594581C211yesmaximal, characteristic, complemented
3#10592456C211yesmaximal, characteristic, complemented
4C3×#4772C211yesmaximal, characteristic, complemented
5C3×#4770C211yesmaximal, characteristic, complemented
6#10591495C211yesmaximal, characteristic, complemented
7#10591463C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10590866C211yesmaximal, characteristic, complemented
10#10590849C211yesmaximal, characteristic, complemented
11#10590825C211yesmaximal, characteristic, complemented
12#10590722C211yesmaximal, characteristic, complemented
13#10590538C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590502C211yesmaximal, characteristic, complemented
16#78935—31nomaximal
17#78855—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#892C2211yescharacteristic
26C3×#892C2211yescharacteristic, complemented
27#63980—21no—
28#63976—21no—
29#63961—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63919C2211yescharacteristic, complemented
32C4×#627—21no—
33#63915—21no—
34#63908C2211yescharacteristic
35C4×#625C2211yescharacteristic
36#63863C2211yescharacteristic
37#63859—21no—
38#63859—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic, complemented
41#63856C2211yescharacteristic
42C2×#3719C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63643C2211yescharacteristic, complemented
46#63642C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5829—31no—
62#5806—31no—
63#5533—31no—
64#5533—31no—
65C3×#418—31no—
66C3×#416—31no—
67#5239—31no—
68#5218—31no—
69#5137—31no—
70#5127—31no—
71#5114—31no—
72#5111—31no—
73#5003—31no—
74#4996—31no—
75#4816—31no—
76#4815—31no—
77#4798—31no—
78#4794—31no—
79#4783—31no—
80#4779—31no—
81#4778—31no—
82#4776—31no—
83#4772D311yescharacteristic, complemented
84#4770D311yescharacteristic, complemented
85#4767—31no—
86#4765—31no—
87#4761—31no—
88#4761—31no—
89#4757—31no—
90#4757—31no—
91#4757—61no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—41no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#627—21no—
108C2×#625—21no—
109C2×#625D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3754—22no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×ΓL(1,𝔽25)—41no—
128C3×D3×C8—41no—
129#3724—21no—
130#3724—21no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3719—41no—
143#3716—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×M16—31no—
150C22×C3×C8—31no—
151C3×#117—31no—
152C3×#117—31no—
153#953—61no—
154C2×#217—61no—
155#947—31no—
156#946—31no—
157C2×#216—31no—
158#939—61no—
159#939—61no—
160#938—31no—
161#937—61no—
162#936—31no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—61no—
171#930—31no—
172#929—61no—
173C4×#67—31no—
174C4×#67—31no—
175C2×(C2×D3)⋊C4—61no—
176#924—31no—
177#924—31no—
178#924—31no—
179C2×Dic12—31no—
180C2×#204—31no—
181C2×ΓL(1,𝔽25)C2×D311yescharacteristic
182C2×D3×C8C2×D311yescharacteristic, complemented
183#897—31no—
184#897—31no—
185#892C2×D311yescharacteristic
186#892C2×D311yescharacteristic, complemented
187#888—31no—
188#888—31no—
189#887—31no—
190#887—31no—
191#887—61no—
192#885—61no—
193#885—61no—
194#879—61no—
195#879—61no—
196#876—61no—
197#876—61no—
198C4×Dic6—61no—
199C4×Dic6—61no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102C2×D311yescharacteristic
208C3×#102C2×D311yescharacteristic
209#835—31no—
210#832—31no—
211#832C2×D311yescharacteristic
212#832C2×D311yescharacteristic
213#830—31no—
214#830—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218#817—31no—
219#817—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223#816C2×D311yescharacteristic, complemented
224#815—31no—
225#815—31no—
226#815—61no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810—31no—
230#810C2×D311yescharacteristic, complemented
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#807—31no—
236#807—31no—
237#807—61no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—81no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254#634—21no—
255#634—21no—
256C3×#67—42no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#627—42no—
273#625—41no—
274#625—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—31no—
293#416—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—121no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—31no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320#237—22no—
321#237—41no—
322D3×D4—22no—
323D3×D4—41no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3C22×D311yescharacteristic
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×M16—121no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—61no—
348C3×C42—61no—
349#217—31no—
350#217—31no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#216—121no—
361#214—64no—
362#214—62no—
363#214—62no—
364#214—121no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—121no—
407#204—121no—
408ΓL(1,𝔽25)—41no—
409D3×C8—41no—
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C22×D4—31no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×M16—31no—
442C22×C8—31no—
443C4⋊Q8—91no—
444#126—181no—
445#126—181no—
446#124—91no—
447#124—181no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452#121—91no—
453#121—181no—
454#120—181no—
455C4×Q8—91no—
456C4×Q8—181no—
457C4×D4—91no—
458C4×D4—91no—
459#117—31no—
460#117—31no—
461C2×C22⋊C4—181no—
462#107—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102D3211yescharacteristic
476C22⋊C8—91no—
477C22⋊C8—91no—
478#97—91no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3—122no—
486C23×C3—122no—
487C23×C3—241no—
488C22×D3—21no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—81no—
492C22×D3D3×D411yescharacteristic
493C22×D3D3×D411yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—22no—
499C3×D4—41no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—122no—
503C3×D4—122no—
504C3×D4#23512yes—
505C3×D4#23512yes—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—42no—
523#67—42no—
524#67—121no—
525#67—121no—
526#67—241no—
527#67—241no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—42no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3—242no—
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549D12—21no—
550D12—21no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555Dic6—21no—
556Dic6—21no—
557Dic6—62no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—121no—
563Dic6—122no—
564Dic6—122no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—62no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C2×C32—42no—
576C2×C32#54611yescharacteristic
577C2×C32#57511yescharacteristic
578C2×C32#57711yescharacteristic
579C3×D3—41no—
580C3×D3—41no—
581C3×D3—81no—
582C24—61no—
583#41—62no—
584#41—121no—
585C2×Q8—31no—
586C2×Q8—91no—
587C2×Q8—181no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—62no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4—121no—
594C2×D4—181no—
595C2×D4C2×D3211yescharacteristic
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—181no—
600Q16—361no—
601SD16—182no—
602SD16—361no—
603M16—121no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8—121no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—61no—
631C42—61no—
632C42—91no—
633C42—181no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—244no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—84no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4C2×#23511yescharacteristic
677C3×C4C2×#23511yescharacteristic
678C3×C4#100411yescharacteristic
679C3×C4#100411yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—121no—
690Dic3—121no—
691Dic3—122no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#331111yescharacteristic, complemented, Sylow
698C23—21no—
699C23—31no—
700C23—31no—
701C23—61no—
702C23—122no—
703C23—122no—
704C23—241no—
705Q8—61no—
706Q8—61no—
707Q8—181no—
708Q8—181no—
709Q8—362no—
710D4—21no—
711D4—61no—
712D4—61no—
713D4—122no—
714D4—122no—
715D4—361no—
716D4—721no—
717D4#379812yes—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—122no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3—121no—
746C2×C3—121no—
747C2×C3—241no—
748C2×C3#549011yescharacteristic
749C2×C3#549011yescharacteristic
750C2×C3#576811yescharacteristic
751C2×C3#577011yescharacteristic
752C2×C3#577311yescharacteristic
753C2×C3#577511yescharacteristic
754D3—41no—
755D3—41no—
756D3—81no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—244no—
770C22D32×D411yescharacteristic
771C4—41no—
772C4—61no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—181no—
779C4—361no—
780C4—361no—
781C4C2×#379811yescharacteristic
782C4#6431311yescharacteristic
783C3—21no—
784C3#7885511yescharacteristic, complemented
785C3#7893511yescharacteristic, complemented
786C2—42no—
787C2—121no—
788C2—121no—
789C2—241no—
790C2#1059418311yescharacteristic
791C2#1059473611yescharacteristic
792C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595244C2
hypercenter#102D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10594581C2semidirect
3. #10592456C2semidirect
4. C3×#4772C2semidirect
5. C3×#4770C2semidirect
6. #10591495C2semidirect
7. #10591463C2semidirect
8. #10591459C2semidirect
9. #10590866C2semidirect
10. #10590849C2semidirect
11. #10590825C2semidirect
12. #10590722C2semidirect
13. #10590538C2semidirect
14. #10590521C2semidirect
15. #10590502C2semidirect
22. #64096C22semidirect
24. C2×C3×D3×C8C22semidirect
26. C3×#892C22semidirect
31. #63919C22semidirect
40. #63857C22semidirect
42. C2×#3719C22semidirect
45. #63643C22semidirect
46. #63642C22semidirect
47. #63634C22semidirect
51. C3×#816C22semidirect
52. C3×#810C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #4772D3semidirect
84. #4770D3semidirect
182. C2×D3×C8C2×D3semidirect
186. #892C2×D3semidirect
223. #816C2×D3semidirect
230. #810C2×D3semidirect
697. C32#3311semidirect
784. C3#78855semidirect
785. C3#78935semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105952442
#105945812
#105924562
C3×#47722
C3×#47702
#105914952
#105914632
#105914592
#105908662
#105908492
#105908252
#105907222
#105905382
#105905212
#105905022
#789353
#788553